It depends if there's a trend for that altcoin. If you check the top crypto you'll see that some altcoins didn't increase much so no matter how much btc price increase if the altcoin's potential is not good then it won't fly high as you said or it's price increasing when btc price increase.
When you say trend, that can mean many of them are affected but a single altcoin can also pump on its own if it have what it takes. Alts like that are not always on the top list or should we say that not all top coins are considered as good coins but there are only factors that pushes them there.
So, we must also be careful on those advices that people should always prioritize the top altcoins. Most of the times BTC is the maker of the alt run when its value is already at its peak and it may not be achieved yet for the altcoins to not follow up. BTC pump, the trend, and the likes, can only be a boost but it will still boil down to the potential of the altcoin if how far it can go.